Time-optimal robotic manipulation on a predefined path of loosely placed objects: Modeling and experiment

A consistent method is presented for solving the so-called general waiter problem, which is to move a tray (mounted at the end-effector of a robot) with a number of loosely placed objects (e.g. cups) as fast as possible such that the objects do not slide at any time. The geometric path of the tray motion is prescribed while the attitude of the tray must vary in order to avoid sliding or tip-over of the objects. The time optimal robot trajectory is determined with a multiple shooting method. For the considered wrist-partitioned robot, the motion is described by the path parameter and the three joint coordinates of the wrist. This 4-parametric description is beneficial for solving the optimal control problem with improved convergence. The optimization takes into account the technical limitations of the robot as well as the limiting friction between objects and tray. Experimental results for a time-optimal motion of a Stäubli RX130L manipulating a tray with 4 cups are presented. A crucial aspect is the use of a model-based control strategy along with the identification of dynamic parameters. Moreover, the basis for any optimization and real-time control is a reliable dynamic model of the robot. Therefore a parameter identification is performed using optimized persistent excitation trajectories. •Consistent method for solving time optimal generalized waiter motion problem.•Dynamics modeling of robot and all constraints for loosely placed objects.•Solution of the optimization problem using multiple shooting.•Implementation in a real hardware.•Experimental validation of the theoretical results.